ENGM032 Coursework Jesus Rodriguez
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Transcript of ENGM032 Coursework Jesus Rodriguez
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ENGM032: COMPOSITE BRIDGE COURSEWORK JESUS RODRIGUEZ RODRIGUEZ
Initial Data
Geometry: Materials:
mm2600Bcarr
Carriageway
2mm
kN205E
s
610200
csshrinkage strain
mm275Ds
2mm
kN31E
csEcs
Es
cs
Slab 6.6129cs
mm50esurf
2mm
kN15.5E
clEcl
Es
cl
Road Surfacing 13.2258cl
m34L Span
2mm
N50f
cu 2mm
N460f
y 2mm
N355
ycmm500C Cantilever
2mm
N345
yfmm2000Spabeam
Beam Spacing
C2Spabeam
B m3B Slab width
Loads:
3m
kN25
c
BDs
c
Wslab
m
kN20.625W
slab
Slab Self Weight
m
kN32W
beam2 Steel Beams Self Weight
3m
kN22
surf
Bcarr
esurf
surf
Wsurf
m
kN2.86W
surf
Road Surfacing
m
kN2.52W
rail2 Parapets
2m
kN5w
live
Bcarr
wlive
Wlive
m
kN13W
live
Footway Live Load
Section Design:
mm330bft
mm20tft
tft
bft
Aft
2mm6600A
ft
Top Flange
mm465bfb
mm25tfb
tfb
bfb
Afb
2mm11625A
fb
Bottom Flange
mm925d mm8tw
tw
dAw
2mm7400A
w
Web Plate
tfb
tft
dD mm970D Steel Beam Height
Ds
DH m1.245H
H
L
27.3092
tw
dw
115.625w
-
Check Shape Limitations:
tft
2
tw
bft
rft
tfb
2
tw
bfb
rfb
8.05rft 9.14r
fb
345
35512r
lim1 345
35512r
lim2
12.1727rlim212.1727r
lim1
Section Classification
355
355tft
7bfo
mm140bfo
Flange is not compact
tft
m.7652ywc
Web in compression for plastic neutral axis, calculated later on
d
tft
ywc
m0.784m
355
355tw1m13
374dlim
mm325.5004dlim
Web is not compact
Calculation of effective areas:
1Kc
No reduction of compression flange
355
355
tw
ywc
rw
93.15rw
No reduction if lower than 68
tw
rw
.006251.425twe
mm6.7425twe
Effective web thickness
twe
tw
tw
dAw
mm6.7425tw
i) Stability During Construction
Lateral Torsional Buckling Analysis
a) Elastic Properties Analysis of the Steel Beam:
Aw
Afb
Aft
D0.5Aw
DAfb
0
ye_s
m0.5846ye_s
12
2D
Aw
2ye_s
D0.5Aw
2ye_s
DAfb
2ye_s
Aft
Is
4m0.0045I
s
Aw
Afb
Aft
As
2m0.0245A
s
-
s
yf
fyd_f
1.11.05s
MPa298.7013fyd_f Design Yield Strength
ye_s
D
fyd_f
Is
Mel_1s
mkN3513.6804Mel_1s
ye_s
fyd_f
Is
Mel_2s
mkN2316.1116Mel_2s
if
else
Mel_2s
Mel_1s
Mel_2s
Mel_1s
Mel_s
mkN2316.1116Mel_s
Elastic Moment Strength for the
Steel Beam
As
Is
rx
m0.4305rx
b) Plastic Properties Analysis for Steel Beam:
s
yc
fyd
2mm
N307.3593f
yd
fyd_f
Afb
Rfb
kN3472.4026Rfb
fyd_f
Aft
Rft
kN1971.4286Rft
fyd
Aw
Rw
kN1916.9424Rw
Rw
Rw
Rft
Rfb
2
dyp_s
m0.8246yp_s
d2
2yp_s
d
Rwd2
2yp_s
Rw
yp_s
Rft
yp_s
DRfb
Mpl_s
mkN2845.542Mpl_s
Plastic Moment Strength for the
Steel Beam
c) Stability Without self-weight of concrete:
Effective LTB length without intermediate restraints:
1k1
1.2k2
1ke
Lke
k2
k1
le
m40.8le
Slenderness Parameter:
2
tfb
tft
tfavg
1k4
1 Llw
-
3tw
d12
13bfb
tfb12
13bft
tft12
1Iy
4m0.0003I
y
Moment of Inertia with respect to Y-axis
As
Iy
ry
m0.1049ry
D
tfavg
ry
lw
F
7.5153F
3bft
tft12
1Icf
4mm
7105.9895I
cf
3bfb
tfb12
1Itf
4mm
8102.0947I
tf
Itf
Icf
Icf
i 0.2224i
From i and F, we obtain the parameter
0.831
k4r
y
le
LT 323.0855LT
Limiting Value of Slenderness:
Mpl_s
Mpe
Mel_s
Mult
Section is not compact
Mult
Mpe
355
35530
lim33.2525
lim
Limiting Moment of Reistance:
Mpe
Mult
355
355LT
R
291.484R
1.2lw
le
0.06 From the graph
Mult
MR
mkN138.9667MR
-
Ultimate Moment due to the Steel Beam Self weight
8
2L
Wbeam
Mbeam
mkN867Mbeam1.10
steel_u
Mbeam
steel_u2
1Mu_2
mkN476.85Mu_2
The beam is not stable, since Mu_2 is larger than Mr We need intermediate Restraints
d) With self-weight of concrete:
Spacing of LTB restraints:
This restraints need to be fully effective, with for example cross
m2.83sLTB
diagonal bracing in plan view, which brace the compression flanges
which are prone to LTB instability during construction, until deck
acts as a restraint
Effective LTB length with intermediate restraints:
Lets say le=lw=lr
sLTB
le
Slenderness Parameter:
2
tfb
tft
tfavg1k
41 l
elw
3tw
d12
13bfb
tfb12
13bft
tft12
1Iy
4m0.0003I
y
As
Iy
ry
m0.1049ry
D
tfavg
ry
lw
F
0.6255F
3bft
tft12
1Icf
4mm
7105.9895I
cf
3bfb
tfb12
1Itf
4mm
8102.0947I
tf
Itf
Icf
Icf
i 0.2224i
F
11.5351.5821.5351
Linear interpolation from BS tablesF
11.2661.2911.2662
-
.2i.1
2
1
1
1.4906
k4r
y
le
LT 40.1983LT
Limiting Value of Slenderness:
Mpl_s
Mpe
1.2286Mult
Mpe
Mel_s
Mult
Mult
Mpe
355
35530
lim33.2525
lim
Limiting Moment of Reistance:
Mpe
Mult
355
355LT
R
36.2665R
1lw
le
.95 From graph
Mult
MR
mkN2200.306MR
Ultimate Moment due to the Steel Beam and Concrete Deck Self weight
8
2L
Wslab
Mslab
8
2L
Wbeam
Mbeam
1.15conc_u1.10
steel_umkN867M
beam
Mbeam
steel_u
Mslab
conc_u2
1Mu_1
mkN2190.5297Mu_1
The beam is stable, since Mr is larger than Mu
ii) Stiffeners:
a) During Construction
No web stiffeners:
La m34a
3
yc
y
MPa204.9593y
MPa355
yc
tw
dw
137.1895w
-
da 36.7568 Web panel ratio
if
else
2
tw
bft
yf
MPa355tft
10
2
tw
bft
yf
MPa355tft
10bfe
tw
2d
yc2
2tft
bfe
yf
mfw
0.0054mfw
From the graph
0.24 y
l
MPa49.1902l
s
l
ld
MPa42.589ld
ld
Aw
Vd
kN265.6193Vd
2
LWslab
conc_u
Wbeam
steel_u2
1Vu_const
kN257.7094Vu_const
There is no need of web stiffeners during construction, since Vd is larger than Vu
b) After Construction
Web stiffeners every 2m:
d
a2
2
m2.00a2
2.16222
From the graph:
0.502
y
2
l2
MPa102.4797l2
s
l2
l2d
MPa88.727l2d
l2d
Aw
V2d
kN553.3736V2d
2
LWsurf
surf_u
Wrail
rail_u
Wlive
live_u
Wslab
conc_u
Wbeam
steel_u2
1Vu
kN517.0019Vu
Design could be optimised, since this maximum shear only occurs close to the supports.
In addition, no bending interaction needs to be checked, since this shear force
occurs where bending moment is equal to zero
-
iii) Ultimate Bending Strength and Ultimate Design Moment
Plastic Moment of Composite Section
Effective Slab Width:
if
else
4
L
Spabeam
Spabeam4
LBeff
m2Beff
C2
Beff
Be
m1.5Be
Ds
Be
Ac
2m0.4125A
c
1.11.05s
s
yc
fyd
2mm
N307.3593f
yd
Steel Design Yield Limit
s
yf
fyd_ff
cu0.45f
cd2
mm
N22.5f
cd
Concrete Design Resistance
Steel Beam Resistance: Concrete Slab Resistance:
fcd
Ac
Rc
kN9281.25Rcf
yd_fAfb
Rfb
kN3472.4026Rfb
fyd_f
Aft
Rft
kN1971.4286Rft
fyd
Aw
Rw
kN1916.9424Rw kN3888.3709R
ftRw
Rw
Rft
Rfb
Rs
kN7360.7735Rs
Plastic Neutral Axis:
Rc is larger than Rs, so PNA lies within the slab depth, as shown in the above figure
DsR
c
Rs
yp
m0.2181yp
yp
0.5D0.5Ds
Rw
yp
0.5Ds
DRfb
yp
0.5Ds
Rft
Mpl
mkN5519.479Mpl
Short-term Mechanical Properties for Elastic Analysis
cs
Ac
Aw
Afb
Aft
cs
Ds
Ac
0.5Ds
D0.5Aw
Ds
DAfb
Ds
Aft
ye1
m0.3409ye1
-
cs
12
2Ds
Ac12
2D
Aw
cs
2Ds
0.5ye1
Ac
2ye1
Ds
D0.5Aw
2ye1
Ds
DAfb
2Ds
ye1
Aft
Ic1
4m0.0141I
c1
Long-term Mechanical Properties for Elastic Analysis
cl
Ac
Aw
Afb
Aft
cl
Ds
Ac
0.5Ds
D0.5Aw
Ds
DAfb
Ds
Aft
ye2
m0.4549ye2
cl
12
2Ds
Ac12
2D
Aw
cl
2Ds
0.5ye2
Ac
2ye2
Ds
D0.5Aw
2ye2
Ds
DAfb
2Ds
ye2
Aft
Ic2
4m0.0119I
c2
Elastic Moment of Composite Section
2
ye2
ye1
ye
2
Ic2
Ic1
Ic
ye
Ds
D
fyd_f
Ic
Mel_1
mkN4578.4589Mel_1
fcdy
e
Ic
avg
Mel_2 2
cs
cl
avg
mkN7282.5148Mel_2
if
else
Mel_2
Mel_1
Mel_2
Mel_1
Mel
mkN4578.4589Mel
Ultimate Design Moment
Load Factors for Combination 1:
At ultimate limit state:
1.15conc_u
1.75surf_u
1.20rail_u
1.10steel_u
1.50live_u
Bending Moments:
8
2L
Wslab
Mslab
mkN2980.3125Mslab
8
2L
Wsurf
Msurf
mkN413.27Msurf
-
82L
Wbeam
Mbeam
mkN867Mbeam
8
2L
Wrail
Mrail
mkN722.5Mrail
8
2L
Wlive
Mlive
mkN1878.5Mlive
Mlive
live_u
Mrail
rail_u
Mbeam
steel_u
Msurf
surf_u
Mslab
conc_u2
1Mu
mkN4394.5159Mu
The section is non-compact, thus Elastic Moment Capacity is to be used
Ultimate Bending Strength is larger than Ultimate Bending Moment
iv) Serviceability Stresses
Dead Load Stresses
Partial Safety Factors at Service
1.00conc_s
1.20surf_s
1.00steel_s
1.00live_s
1.00rail_s
Dead Load Bending Moment
Mrail
rail_s
Mbeam
steel_s
Msurf
surf_s
Mslab
conc_s2
1MDL
mkN2532.8682MDL
We will use the mechanical properties for long-term loading, since dead loads are
permanent loads
ye2
y1
Ds
ye2
y2
mm.00001y2
y3
m0y4
Ds
Dye2
y5
cl
Ic2
y1
MDL
1_d
clIc2
y2
MDL
2_d I
c2
y3
MDL
3_d I
c2
y4
MDL
4_d I
c2
y5
MDL
5_d
mm.001y5
y5
y4
y3
y2
y1
mm.001y1
yDL
0
5_d
4_d
3_d
2_d
1_d
0
XDL
m0.7901
m0.7901
0
m0.1799
m0.1799
m0.4549
m0.4549
yDL
MPa
0
168.4658
0
38.3633
2.9006
7.3342
0
XDL
-
Dead Load Stresses Graph
M1
-256 -128 0 128
0.5
0.25
0
-0.25
-0.5
-0.75
-1
x
y
Live Load Stresses
Dead Load Bending Moment
Mlive
live_s2
1MLL
mkN939.25MLL
We will use the mechanical properties for short-term loading, since live load is an
instantaneous load
ye1
y1_l
Ds
ye1
y2_l
mm.00001y2_l
y3_l
m0y4_l
Ds
Dye1
y5_l
cs
Ic1
y1_l
MLL
1_l
csIc1
y2_l
MLL
2_l I
c1
y3_l
MLL
3_l I
c1
y4_l
MLL
4_l I
c1
y5_l
MLL
5_l
mm.001y5_l
y5_l
y4_l
y3_l
y2_l
y1_l
mm.001y1_l
yLL
0
5_l
4_l
3_l
2_l
1_l
0
XLL
m0.9041
m0.9041
0
m0.0659
m0.0659
m0.3409
m0.3409
yLL
MPa
0
60.2705
0
4.3943
0.6645
3.4368
0
XLL
-
Live Load Stresses Graph
M2
-96 -64 -32 0 32
0.5
0.25
0
-0.25
-0.5
-0.75
-1
x
y
Total Load Stresses
Ic1
ye1
ye2
MLL
4
mm.001y5
y5
y4
y3
y2
y1
mm.001y1
yTL
0
5_l
5_d
4
4_d
3_l
3_d
2_l
2_d
1_l
1_d
0
XTL
m0.7901
m0.7901
0
m0.1799
m0.1799
m0.4549
m0.4549
yTL
MPa
0
228.7363
7.5999
42.7575
3.5651
10.7709
0
XTL
Total Load Stresses Graph
M3
-256 -128 0 128
0.5
0.25
0
-0.25
-0.5
-0.75
x
y
-
v) Stresses due to shrinkage
Restrained Shrinkage stresses
cs
Ecl
fo
MPa3.1fo
Restrained Tensile Stress in the slab
Balancing Forces
Ac
fo
Fsh
kN1278.75Fsh
Compression Balancing Force
Ds
0.5ye2
Fsh
Msh
mkN405.8989Msh Sagging Balancing Moment
Balancing Axial Stresses
Aw
Afb
Aft
cl
Ac
Acomp Area Composite Section
Acomp
Fsh
f1
MPa22.9781f1
Balancing Axial Stress in Steel
cl
f1
f1c
MPa1.7374f1c
Balancing Axial Stress in Concrete
Balancing Bending Stresses
Ic2
Ds
ye2
Msh
f2tf
MPa6.1478f2tf Top Flange, in steel
cl
f2tf
f2bs_c
MPa0.4648f2bs_c Bottom Slab, in concrete
cl
Ic2
ye2
Msh
f2ts_c
MPa1.1753f2ts_c Top Slab in concrete
Ic2
Ds
Dye2
Msh
f2bf
MPa26.9971f2bf
Bottom Flange
Final Stresses
f2ts_c
f1c
fo
ft_conc
MPa0.1873ft_conc
Tensile stress top of slab
f2bs_c
f1c
fo
fb_conc
MPa0.8978fb_conc
Tensile stress bottom of slab
f1
f2tf
ftf
MPa29.1259ftf
Compression stress on tof flange
f1
f2bf
fbf
MPa4.019fbf
Tensile stress on bottom flange
Ds
Dy1
Dy2
mm.0001Dy3
m0y4
-
mm0001y4
y4
y3
y2
y1
mm.001y1
ysh
0
fbf
ftf
fb_conc
ft_conc
0
Xsh
m0.001
0
m0.97
m0.97
m1.245
m1.245
ysh
MPa
0
4.019
29.1259
0.8978
0.1873
0
Xsh
Shrinkage Induced Stresses Graph
M4
-32 -16 0 16 32
1.25
1
0.75
0.5
0.25
0 x
y
vi) Stud Connectors
Plastic design
Longitudinal shear force Rq between the steel and concrete:
if
else
Rc
Rq
Rs
Rq
Rc
Rs
Rq
kN7360.7735Rq
114Ns
Total Number of Studs in Half Span mm16stud
Diameter
mm75hstud
HeightkN820.8N
sRstuds
kN7478.4Rstuds
Total Stud Strength
2
Ns
2
L
ssc
mm298.2456ssc
Spacing if arranged in pairs
stud
4stud
2mm20bflange_min
m0.12bflange_min
Minimum flange width
-
57 pairs of 16mm studs for half span
Let's check for elastic design:
Stud resistance per unit length
ssc
kN82.82R
m
kN439.9059R
Longitudinal shear force q between the steel and concrete:
cl
Ic1
2
Ds
ye1
Ac
Vu
q m
kN232.8055q
Studs are OK